Large deviations for Markov processes via Hamilton-Jacobi-Bellman equations
We consider the context of two-component Markov processes modelling biochemical phenomena, such as the motion of motor proteins or chemical reactions involving enzymatic molecules. Rescaling the process in space and time and taking into account the limit of the rescaling factor tending to infinity, we prove path-wise large deviations for the "slow"-variable of the process. The large deviations principle is established using a method developed by J. Feng and T. G. Kurtz, based on the analysis of an associated Hamilton-Jacobi-Bellman equation. The talk is based on two joint works with Richard Kraaij.
Area: IS15 - Stochastic processes in the natural sciences (Giuseppe D'Onofrio/ Serena Spina)
Keywords: Large deviations, multi-scale Markov processes, Hamilton-Jacobi-Bellman equations, viscosity solutions
Please Login in order to download this file